Final answer:
The correct answer is the conditional probability of event B given event A, P(B|A), which is calculated using the formula P(A and B) / P(A). Using the provided probabilities, P(B|A) is determined to be 0.60.
Step-by-step explanation:
The student is asking about the concept of conditional probability, specifically they need to find the probability of event B given that event A has occurred, which is denoted as P(B|A). The formula to calculate this is P(B|A) = P(A and B) / P(A).
Given that P(A) = 0.45, P(B) = 0.63, and P(A and B) = 0.27, we plug these values into the formula to find P(B|A).
So, P(B|A) = P(A and B) / P(A) = 0.27 / 0.45.
Now performing the division we get:
P(B|A) = 0.6.
The answer to the student's question is option d) 0.60.